Freeform surfaces containing multiple curvatures, such as aspheres, present challenges for optical measurement. For example, freeform test surfaces that depart from spheres or planes present problems relating to both the range of measurement and the accuracy with which the freeform surfaces can be measured. Particularly for purposes of wavefront measurements, illumination is generally intended to be directed at normal incidence to the freeform surfaces for collecting retroreflected light from the freeform surfaces. Departures of illumination wavefront shapes from the intended shapes of the freeform surfaces can exceed the range of measurement and introduce measurement errors.
Measuring instruments, particularly those that exploit the mechanism of interference, generally have limited ranges of measurement. Even relatively small departures of the shape of freeform surface from the shape of the illumination wavefront can exceed the dynamic range of the measuring instruments. For example, the fringe spacing of interference patterns representing differences between the shapes of the freeform surface and a reference surface modeled by the illumination wavefront rapidly decreases with increasing differences between the shapes, rendering the interference patterns ambiguous or indecipherable.
Shaping the illumination wavefronts to more closely match the intended shape of the test objects can be difficult to accomplish. Wavefront shaping optics must be changed to accommodate different freeform shapes of the test objects. The substitution of different shaping optics is expensive and difficult to calibrate. The use of adjustable shaping optics can lead to errors or loss of accuracy, especially where the contributions of the shaping optics must be monitored to account for the changes of wavefront shape. The contributions of the shaping optics to the reference against which the freeform surfaces are compared are often difficult to determine, especially when subject to change, and can introduce various types of errors as well as ambiguities that are difficult to resolve to desired accuracy.
Some measuring instruments produce conventional illumination wavefronts, e.g., spherical wavefronts, and match the curvature of the illumination wavefronts to limited size zones of the freeform surfaces. Measurements of the limited zones of the freeform surfaces are stitched together to provide overall measurements of the freeform surfaces. This approach has been used for measuring rotationally symmetric test surfaces, where the limited zones have an annular form. However, non-rotationally symmetric test surfaces and other surface shapes that depart more significantly from a conventional form can require the measurement zones to be so small that an inordinate number of measurement zones must be acquired, thereby increasing measurement time, adding complexity of the measurements, and reducing overall accuracy, which can be compromised by additional variables associated with stitching the many zonal measurements together.